H*(As(K)) = H*(A-s(K)) for all sand
H*(As(K)) = Z for s ≥ m.The calculation of H*(As(K)) is done using the model for knot Floer complexes coming from grid diagrams; see , , , . In fact, the code is inspired from the program  for computing the usual knot Floer homology.
cabal install Vectorand
cabal install Repaat your terminal. If you have trouble installing Repa, try typing
cabal install repa-220.127.116.11instead.
ghc --make -O2 ASHat.hs -XBangPatterns -XTypeOperators -XTypeSynonymInstancesto compile the program.
./ASHat "[4, 0, 1, 2, 3]" "[1, 2, 3, 4, 0]". This is the left-handed trefoil. The first list corresponds to X's and the second corresponds to O's. The origin of the grid is the lower left hand corner.
This means that for s=0 the homology is of rank 2 in relative grading 0
and rank 1 in relative grading 1. For s=1 (and in fact for any other
nonzero s) the homology is of rank 1.
If you are interested in developing the program, contact us!
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 C. Manolescu and P. Ozsvath, Heegaard Floer homology and integer surgeries on links, preprint (2010).
 C. Manolescu, P. Ozsvath and D. Thurston, Grid diagrams and Heegaard Floer invariants, preprint (2009).